Nash equilibrium is a concept in game theory in which every participant in a non-cooperative game can optimize their outcome based on the other players’ decisions. It can be used to model economic behavior to predict the best response to any given situation. What is Nash Equilibrium?
History of Nash equilibrium
The theory of the pure-strategy Nash equilibrium, or finding the optimal strategy for each player in a game, was developed as a concept before John Nash fully defined it, but it would also go on to be iterated on and developed to be more accurate and more widely applicable.
- John Nash’s equilibrium, defined by John Nash, was a major development in game theoretics and would later be refined by other theorists.
Nash Equilibrium Examples
The prisoner’s dilemma: Two criminals are placed in separate rooms and must decide whether to testify against their partner and convict them or remain silent. If they both betray each other, they each serve two years in prison.
- Matching pennies: Two players must secretly turn a penny to heads or tails and then reveal their penny. If the pennies are matching, player A keeps both pennies while player B keeps one, and if they don’t match, both keep one. This is an example of a pure-strategy Nash equilibrium.
How to Find Nash equilibrium
To find Nash equilibrium, share each player’s strategy with every other player. If the players do not change their strategies, you have found the Nash equilibrium.
- Use tables to map each set of strategies
- There are two possible Nash equilibria: Both players choose ballet, or both players choose prizefight
